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Q 1. If {tex} \sin \theta + \cos \theta = \sqrt { 2 } \cos \left( 90 ^ { \circ } - \theta \right) {/tex} then {tex} \cot \theta {/tex} is equal to
{tex} \frac { 1 } { \sqrt { 2 } } {/tex}
{tex} \frac { \sqrt { 3 } } { 2 } {/tex}
{tex} \frac { 1 } { \sqrt { 2 } - 1 } {/tex}
{tex} \sqrt { 2 } - 1 {/tex}
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Q 2. If {tex} \sec \theta + \tan \theta = x {/tex} then the value of {tex} \sec \theta - \tan \theta {/tex} is equal to
{tex} - x {/tex}
{tex} \frac { 1 } { x } {/tex}
{tex} - \frac { 1 } { x } {/tex}
{tex} \sqrt { x } {/tex}
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Q 3. If {tex} \mathrm { x } = \mathrm { a } \sin \theta {/tex} and {tex} \mathrm { y } = \mathrm { b } \cos \theta , {/tex} then the value of {tex} \mathrm { b } ^ { 2 } \mathrm { x } ^ { 2 } + \mathrm { a } ^ { 2 } \mathrm { y } ^ { 2 } {/tex} is
{tex} \mathrm{a ^ { 2 } b ^ { 2 }} {/tex}
{tex}\mathrm{ a b} {/tex}
{tex} \mathrm{\frac { 1 } { a ^ { 2 } b ^ { 2 } }} {/tex}
{tex} \mathrm {\frac { 1 } { \mathrm { ab } }} {/tex}
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Q 4. An equation is called an identity if
If is true for all values of variable
Not for all values of variabls but some value of variable
Exactly one value of variables
Exactly two value of variables
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Q 5. If {tex} x = ( \sec A + \tan A ) ( \sec B + \tan B ) ( \sec C + \tan C ) ; y = ( \sec A - \tan A ) ( \sec B - \tan B ) ( \sec C - \tan C ) {/tex} and {tex} x = y {/tex} then {tex} x {/tex} and {tex} y {/tex} is equal to
{tex} \pm 1 {/tex}
{tex}0{/tex}
{tex} \pm 2 {/tex}
None of these
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Q 6. If {tex} x = \cot ^ { 2 } \theta - \frac { 1 } { \sin ^ { 2 } \theta } {/tex} than the value of {tex} x {/tex} is
{tex} 1 {/tex}
{tex} - 1 {/tex}
{tex} \pm 1 {/tex}
zero
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Q 7. {tex} 2 \left( \sin ^ { 6 } \theta + \cos ^ { 6 } \theta \right) - 3 \left( \sin ^ { 4 } \theta + \cos ^ { 4 } \theta \right) {/tex} is equal
zero
1
-1
None of these
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Q 8. {tex} \sqrt { \frac { 1 + \sin \theta } { 1 - \sin \theta } } {/tex} is equal to
{tex} \sec \theta + \tan \theta {/tex}
{tex} \sec \theta - \tan \theta {/tex}
{tex} \sec ^ { 2 } \theta + \tan ^ { 2 } \theta {/tex}
{tex} \sec ^ { 2 } \theta - \tan ^ { 2 } \theta {/tex}
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Q 9. {tex} \sec ^ { 4 } A - \sec ^ { 2 } A {/tex} is equal to
{tex} \tan ^ { 2 } A - \tan ^ { 4 } A {/tex}
{tex} \tan ^ { 4 } A - \tan ^ { 2 } A {/tex}
{tex} \tan ^ { 4 } A + \tan ^ { 2 } A {/tex}
{tex}- \tan ^ { 2 } A - \tan ^ { 4 } A {/tex}
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Q 10. {tex} \cos ^ { 4 } A - \sin ^ { 4 } A {/tex} is equal to
{tex} 2 \cos ^ { 2 } A + 1 {/tex}
{tex} 2 \cos ^ { 2 } A - 1 {/tex}
{tex} 2 \sin ^ { 2 } - 1 {/tex}
{tex} 2 \sin ^ { 2 } A + 1 {/tex}
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Q 11. {tex} \mathrm { P } = ( 1 + \cot \theta - \cosec \theta ) ( 1 + \tan \theta + \sec \theta ) {/tex}
the value of {tex}\mathrm P {/tex} is equal to
1
2
4
zero
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Q 12. {tex} ( \cosec \theta - \sin \theta ) ( \sec \theta - \cos \theta ) ( \tan \theta + \cot \theta ) {/tex} is equal to
zero
1
-1
none of these
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Q 13. The value of 
is equal to:
{tex} \sqrt { 3 } {/tex}
{tex} - \sqrt { 3 } {/tex}
{tex} \frac { 1 } { \sqrt { 3 } } {/tex}
{tex} - \frac { 1 } { \sqrt { 3 } } {/tex}
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Q 14. The expression {tex} \sqrt { \sin ^ { 2 } ( 37.5 ) ^ { \circ } + \cos ^ { 2 } ( 37.5 ) ^ { \circ } } + \sqrt { \cos ^ { 2 } ( 37.5 ) ^ { \circ } + sin ^ { 2 } ( 37.5 ) ^ { \circ } } {/tex} simplifies to:
an irrational number
a prime number
a natural number which is not composite
a real number of the form {tex} a + \sqrt { b } {/tex}
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Q 15. If {tex} 15 \cos ^ { 4 } \alpha + 10 \sin ^ { 4 } \alpha = 6 , {/tex} then the value of {tex}8 \sec ^ { 6 } \alpha + 27 \cosec ^ { 6 } \alpha {/tex} is
200
250
220
None of these
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Q 16. If {tex} a = \frac { \cot \theta } { \cot \theta - \cot 3 \theta }\ \ \& \ b = \frac { \tan \theta } { \tan \theta - \tan 3 \theta } {/tex} then {tex} \sqrt { a + b } {/tex} is equal to
{tex} \pm 2 {/tex}
{tex} - 2 {/tex}
{tex} + 1 {/tex}
{tex} - 1 {/tex}
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Q 17. If {tex} a \cos \theta - b \sin \theta = C {/tex} then {tex} a \sin \theta + b \cos \theta = {/tex}
{tex} \pm \sqrt { a ^ { 2 } + b ^ { 2 } + c ^ { 2 } } {/tex}
{tex} \pm \sqrt { a ^ { 2 } + b ^ { 2 } - c ^ { 2 } } {/tex}
{tex} \pm \sqrt { c ^ { 2 } - a ^ { 2 } - b ^ { 2 } } {/tex}
None of these
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Q 18. If {tex} a \cos \theta + b \sin \theta = 4 {/tex} and {tex} a \sin \theta - b \cos \theta = 3 {/tex} then {tex} \left( a ^ { 2 } + b ^ { 2 } \right) {/tex} is equal to
7
12
25
None of these
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Q 19. If {tex} \cos A = \frac { 4 } { 5 } {/tex} then the value of {tex} \tan A {/tex} is :
{tex} \frac { 3 } { 5 } {/tex}
{tex} \frac { 3 } { 4 } {/tex}
{tex} \frac { 4 } { 3 } {/tex}
{tex} \frac { 1 } { 8 } {/tex}
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Q 20. The value of the expression [cosec {tex} \left( 75 ^ { \circ } + \theta \right) {/tex} {tex} \left. - \sec \left( 15 ^ { \circ } - \theta \right) - \tan \left( 55 ^ { \circ } + \theta \right) + \cot \left( 35 ^ { \circ } - \theta \right) \right] {/tex} is :
{tex} - 1 {/tex}
{tex} 0 {/tex}
{tex} 1 {/tex}
{tex} \frac { 3 } { 2 } {/tex}
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Q 21. Given that {tex} \sin \theta = \frac { a } { b } {/tex} then {tex} \cos \theta {/tex} is equal to
{tex} \frac { b } { \sqrt { b ^ { 2 } - a ^ { 2 } } } {/tex}
{tex} \frac { b } { a } {/tex}
{tex} \frac { \sqrt { b ^ { 2 } - a ^ { 2 } } } { b } {/tex}
{tex} \frac { a } { \sqrt { b ^ { 2 } - a ^ { 2 } } } {/tex}
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Q 22. The value of (tan {tex} \left. 1 ^ { \circ } \tan 2 ^ { \circ } \tan 3 ^ { \circ } \dots \tan 89 ^ { \circ } \right) {/tex} is :
{tex} { 0 } {/tex}
{tex}1{/tex}
{tex}2{/tex}
{tex} \frac { 1 } { 2 } {/tex}
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Q 23. If {tex} \Delta A B C {/tex} is right angled at {tex} C , {/tex} then the value of {tex} \cos {/tex} {tex} ( A + B ) {/tex} is :
{tex} 0{/tex}
{tex} 1{/tex}
{tex} \frac { 1 } { 2 } {/tex}
{tex} \frac { \sqrt { 3 } } { 2 } {/tex}
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Q 24. If {tex} \sin A + \sin ^ { 2 } A = 1 , {/tex} then the value of the expression {tex} \left( \cos ^ { 2 } A + \cos ^ { 4 } A \right) {/tex} is :
{tex} 1{/tex}
{tex} \frac { 1 } { 2 } {/tex}
{tex} 2{/tex}
{tex} 3{/tex}
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Q 25. Given that {tex} \sin \alpha = \frac { 1 } { 2 } {/tex} and {tex} \cos \beta = \frac { 1 } { 2 } {/tex}, then the value of {tex} ( \alpha + \beta ) {/tex} is :
{tex} 0 ^ { \circ } {/tex}
{tex} 30 ^ { \circ } {/tex}
{tex} 60 ^ { \circ } {/tex}
{tex} 90 ^ { \circ } {/tex}
